Pipe and tool for thermal cracking of hydrocarbons

Abstract

The invention relates to a tube for the thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is guided through externally heated tubes, in which the tube extends along a longitudinal axis and has a number NT of grooves inserted into the inner surface of the tube and extending in a spiral around the longitudinal axis along the inner surface, the inner surface in which the grooves, in a cross-section at right angles to the longitudinal axis, have a diameter Di and a radius 2 / Di = r1, the grooves in the cross-section in At right angles to the longitudinal axis, at the base of their groove, each has the shape of a circular arc, the circular arc having a radius r2, and the grooves each have a groove depth TT which, in the cross-section at right angles to the longitudinal axis, corresponds in each case to the smallest distance between a circle with diameter Di on which the inner surface lies and its centre lying on the longitudinal axis, and the furthest removed point of the groove base from the groove from the longitudinal axis.

Description

"A tube and device for the thermal fission of hydrocarbons" The invention relates to a tube for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is conducted externally through heated tubes. The invention further relates to an apparatus for thermal cracking of hydrocarbons. For the high-temperature pyrolysis of hydrocarbons (mineral oil derivatives), tube furnaces have been found to be useful, in which a hydrocarbon / steam mixture at temperatures above 750 °C is conducted through rows of individual tubes or tubes in a tortuous arrangement (broken tube coils) made of a heat-resistant nickel-chromium-iron alloy with high oxidation / scaling resistance and high carburization resistance. The tube coils consist of straight tube sections extending vertically or horizontally and connected to each other by U-shaped tube bends or arranged parallel to each other. They are usually heated with the aid of wall burners and / or additionally with the aid of base burners and thus have a "light side" opposite the burners and a "dark side" offset by 90 °C, i.e. continuous in the direction of the tube rows. The mean tube wall temperatures (TMT) here are in some cases greater than 1000°C. The life of the fracture tubes depends to a large extent on the creep and carburization resistance and on the carbonization rate of the tube material. The important factors for the carbonization rate, i.e. for the growth of a layer of carbon deposits (pyrolysis coke) on the inner wall of the tube, are not only the type of hydrocarbons used but also the gas cracking temperature in the inner wall area and what is called the cracking intensity, which captures the effect of the system pressure and residence time in the tube system on the ethylene yield. The cracking intensity is set using the average outlet temperature of the cracking gases (e.g. 850˚C). The higher the gas temperature in the vicinity of the inner wall of the tube above this temperature, the more important the growth of the pyrolysis coke layer will be, the insulating effect of which causes the tube wall temperature to rise further.Although the nickel-chromium-iron alloy with 0.4% carbon, more than 25% chromium and more than 20% nickel, for example 35% chromium, 45% nickel and optionally 1% niobium, used as the tube material has a high carburization resistance, carbon penetrates into the tube wall in defects in the oxide layer, leading to significant carburization that can extend to carbon contents of 1% to 3% at wall depths of 0.5 mm to 3 mm. This is associated with a significant brittleness of the tube material with a risk of cracking under the stress of thermal cycling, especially at furnace start-up and shutdown. To destroy the carbon deposits (coking) on ​​the inner wall of the tube, it is necessary to stop the cracking operation from time to time and burn off the pyrolysis coke with the help of a steam / air mixture. This requires an operational interruption of up to 36 hours and therefore significantly impairs the economic efficiency of the process. British Patent Specification 796 969 and European Patent Specification 1A 541 136 1 also disclose the use of fracture tubes with internal fins. Although such internal fins provide a larger internal surface area by a large percentage, for example 10% larger, and hence result in better heat transfer, they also come with the disadvantage of a significant increase in pressure drop compared to a smooth tube due to friction on the increased internal surface area of ​​the tube. The higher pressure drop requires a higher system pressure, and hence inevitably changes the residence time and worsens the efficiency. An additional factor is that known tube materials with high carbon and chromium contents cannot be profiled by cold forming, for example cold drawing. They have the disadvantage that their ductility is significantly reduced with increasing thermal resistance. The effect has been that temperatures above the tube wall of up to 1050°C, for example, are desirable, which requires the use of centrifuge-cast tubes due to the ethylene yield.However, because centrifugally cast tubes can only be made with a cylindrical wall, special forming methods are required, for example an electrolytic material-removal processing operation or a shape-derived welding method, to produce the inner tubes. Finally, the specification of US patent 718 950 5 also discloses a full range of inclination angles as well as distances between the inner blades, but without considering the specifications of the blades. 9B 289 525 1 EP discloses a finned tube for thermal cracking of hydrocarbons having spiral internal fins inclined relative to the tube axis. 1A 043375 / 2010 WO discloses a nickel-chromium-iron alloy having a high oxidation resistance and carburization resistance, tear strength and creep resistance, comprising 0.4% to 0.6% carbon, 28% to 33% chromium, 15% to 25% iron, 2% to 6% aluminum, up to 2% silicon, up to 2% magnesium, up to 1.5% niobium, up to 1.5% tantalum, up to 0.1% tungsten, up to 0.1% titanium, up to 0.1% zirconium, up to 0.5% yttrium, up to 0.5% cerium, up to 0.5% molybdenum, up to 0.1% nitrogen, balance: nickel containing smelting impurities. Against this background, an object of the invention is to improve the economic efficiency of the thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. This object is achieved by the subject matter of claims 1, 2, 9 and 10. Advantageous embodiments are provided in the dependent and explanatory claims which follow. It has been found that, in a pipe having the preliminary features of claim 1, there is a relationship between the features that characterize the pipe, namely The number of NT grooves inserted into the inner surface of the tube and extending in a spiral around the longitudinal axis along the inner surface, Diameter of the inner surface area where the grooves are inserted, in a cross-section, at right angles to the longitudinal axis, R2 groove base radius of grooves each having a circular arc shape at the base of their groove and located at right angles in the cross-section to the longitudinal axis, and  Groove depth TT grooves which, in a cross-section at right angles to the longitudinal axis, correspond in each case to the smallest distance between a circle with diameter Di on which the inner surface lies and whose centre lies on the longitudinal axis, and the furthest removed point of the groove base from the groove from the longitudinal axis, which can be considered to improve the economic efficiency of thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. To understand, it has been established that it is possible to determine a characteristic value based on heat transfer considerations which can be calculated in two different ways, each of which, however, depends solely on the aforementioned characteristics that characterize the pipe. Based on an initial heat transfer consideration, this characteristic value can be expressed as follows: P1 * |Deqv|2+ P2 * |Deqv| + P3 With constants P1, P2 and P3 and the numerical value |Deqv|, the equivalent diameter Deqv depends on the measured inner diameter Di in mm. Good results are obtained when the constant P1 is a number selected from the claimed range of -0.2 to -0.3. In a preferred embodiment, the constant P1 is selected from a range of -0.25 to -0.295, particularly preferably from a range of -0.287 to -0.2655. Particularly preferably, the constant P1 is equal to -0.287 or -0.2655. Good results are obtained when the constant P2 is selected from a claimed range of 310 to 315. In a preferred embodiment, the constant P2 is selected from a range of 310 to 312, particularly preferably from a range of 42 / 310 to 31 / 311. Particularly preferably, the constant P2 is equal to 42 / 310 or 31 / 311. Good results are obtained when the constant P3 is selected from a claimed range of 200 to 1500. In a preferred embodiment, the constant P3 is selected from a range of 230 to 1400, particularly preferably from a range of 21 / 261 to 1076. Particularly preferably, the constant P3 is equal to 21 / 261 or 1076. The characteristic value used according to the invention for the pipe configuration is expressed in the above relationship as a function of the numerical value |Deqv| of the equivalent diameter Deqv, which depends on the inner diameter Di measured in mm. The term "numerical value" is understood in this text and in the rest of the documentation to mean a dimensionless number of a value of a physical parameter, which is composed of a numerical value and a unit of measurement. A physical parameter is a quantifiable property of an object, process or physical state. Its value (size) is reported as the product of a numerical value (measured value) and a unit of measurement. Since the relationships used according to the invention for the pipe configuration are dimensionless, the numerical value of the physical parameters is used. For the sake of clarity, the numerical value of a parameter is expressed in the description and claims by a name, otherwise it is often used to represent a quantity, for example |Deqv|. The representation of a variable between two horizontal lines, for example |Deqv|, is understood in the context of this description and claims to be a numerical value representation of the value (size) of a physical parameter expressed by the variable.The numerical value |Di| of a diameter Di expressed in mm is 70 mm, for example, the number 70. The characteristic value used for the configuration of the tube according to the invention is expressed in the above relationship as a function of the numerical value |Deqv| of the equivalent diameter Deqv which depends on the internal diameter Di measured in mm. The equivalent diameter is the internal surface area which a smooth, ungrooved tube has a passage area corresponding to the passage area of ​​the inventive tube. The passage area is understood to mean the free area inside the tube in a cross-section at right angles to the longitudinal axis. It has been found that considerations based on heat transfer can often be made more easily in a smooth tube. It has also been found that users of the inventive tube, in their plants for the thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is conducted through externally heated tubes, have in the past often worked with smooth tubes. To switch to the inventive tubes, it is therefore easier if a comparison with the smooth tube of the corresponding passage area can be made. The equivalent diameter Deqv is obtained from the radius of the inner surface area by the relation Deqv = 2 reqv, which is obtained from a smooth, ungrooved pipe having a passage area corresponding to the passage area of ​​the inventive pipe. If the passage area Aeqv of the smooth pipe (Aeqv = π (reqv)2) is equal to the passage area of ​​the inventive pipe, the passage area Aeqv of the smooth pipe may be expressed as follows in the characteristics that characterize the pipe (the symbols used correspond to a nomenclature that is also specified as an example method in Figure 5): The passage area of ​​the inventive pipe, which is equal to the passage area Aeqv of the smooth pipe, is composed of the passage area A1 limited by the area of ​​the inner surface in which the grooves are inserted, which can be easily determined from the radius of the inner surface by A1 = π r12, and the additional areas provided by the number of grooves NT with their corresponding passage areas AT. After solving the above equation, the passage area of ​​the inventive pipe, which is equal to the passage area Aeqv of the smooth pipe, can therefore be expressed as follows, exclusive of the properties that characterize the pipe (also denoted hereinafter as formula (1)): According to a second consideration of heat transfer, this characteristic value can be described as follows: C1 + C2 * |TT| + C3 * VD + C4 * |Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv| – C8) * C9 Or, taking into account further connections, as C1 + C2 * |TT| + C3 * VD + C4 * | Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv| – C8) * C9 + (VD – C6) * (| Deqv| – C8) * C10 + (| Deqv| – C8) * (| Deqv| – C8) * C11 As a function of the numerical value |Deqv| the equivalent diameter Deqv depends on the inner diameter Di measured in mm, the number of grooves NT and the numerical value |TT| the groove depth TT measured in mm and the groove density VD which is the ratio of grooves NT in the pipe to the reference number Nref the maximum number of grooves with a groove depth TT = 1.3 mm that can be inserted into the inner surface area of ​​a pipe with an equivalent diameter Deqv. The constants are fixed here as follows: C1 = 066 / 1946 C2 = 378 / 302 C3 = -178 / 2 C4 = 002 / 266 C5 = 954 / 1 C6 = 495 / 50 C7 = -2 / 004 C8 = 732 / 79 C9 = -1 / 041 C10 = 0.04631 C11 = 26550 / 0 It is known that, if these two calculation methods are equal for the characteristic value, the relationship P1 * |Deqv|2+ P2 * |Deqv| + P3 = C1 + C2 * |TT| + C3 * VD + C4 * |Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv| – C8) * C9 Or, taking into account further connections, the relationship P1 * | Deqv|2+ P2 * |Deqv| + P3 = C1 + C2 * |TT| + C3 * VD + C4 * | Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv| – C8) * C9 + (VD – C6) * (| Deqv| – C8) * C10 + (| Deqv| – C8) * (| Deqv| – C8) * C11 It is obtained as a description of the relationship of tube defining characteristics to each other, which defines a tube that improves the economic efficiency of thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. Tube defining characteristics that are specifically used for the tube, namely The number of NT grooves inserted into the inner surface of the tube and extending in a spiral around the longitudinal axis along the inner surface, Diameter of the inner surface area where the grooves are inserted, in a cross-section, at right angles to the longitudinal axis, R2 groove base radius of grooves each having a circular arc shape at the groove base and located at right angles in cross-section to the longitudinal axis, and  Groove depth TT grooves which, in a cross-section at right angles to the longitudinal axis, correspond in each case to the smallest distance between a circle with diameter Di on which the inner surface lies and whose centre lies on the longitudinal axis, and the furthest removed point of the groove base from the longitudinal axis of the groove, It can be achieved by simple iterations based on this relationship. Each pair of these four tube characteristics that satisfies this relationship will produce a tube that improves the economic efficiency of thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. In practice, it turns out that the work involved in repetition can be reduced even further in practice. For example, the findings for unique characteristics among the four factors that characterize the tube arise from rigidity or manufacturing constraints or else from the need to produce a tube with a specific passage area. The maximum possible weight of a single pipe resulting from the plant in which the pipe is to be used may cause a limitation on the maximum wall thickness of the pipe, which in turn results in a limitation on the maximum depth of the TT groove that can be produced from stiffness aspects. Limitations in terms of wall thickness (and therefore in terms of the maximum depth of the groove that can be produced) may also arise from other aspects, for example from the heat transfer that must be achieved. Stiffness considerations may also result in an upper limit on the number of grooves NT inserted into the inner surface of the pipe and extending in a spiral around the longitudinal axis along the inner surface in combination with the groove depth TT. If an additional number of grooves are inserted too deeply, the pipe stiffness may be excessively weakened. It is also possible that the limitations on the radius r2 of the circular arc of the groove base in combination with the groove depth TT arise from the tendency of the tube to coke in the thermal cracking of hydrocarbons in the presence of steam, where the feed mixture is directed through externally heated tubes. Furthermore, limitations arise from production aspects, for example with regard to the radius r2 of the circular arc of the groove base in combination with the groove depth TT. The grooves may, for example, be produced by a deep-hole drilling method, for example in the method described in German patent application No. 7.907 012 2016 10, which has been filed by the applicant but has not yet been published. This is done by using replaceable cores for producing the grooves. These replaceable cores are available in fixed sizes. If – as is recommended for reasons of economic efficiency – currently available replaceable cores are used, the distribution with such a possible option of special production of replaceable cores for the production of special pipes, this also leads to adjustments for the radius r2 of the circular arc of the groove base in combination with the groove depth TT.It may also be assumed that it is the case that a tube with a first number of grooves can be produced more quickly and at less cost than a tube with a second number of grooves compared to the first number, and so this too can place a limit on the number of grooves that must be inserted. Limitations can also arise from the fact that a certain throughput of feed mixture is required for the pipe and, therefore, a minimum pipe passage area. The result is that, before the iteration is performed, there are already ranges where unique features cannot be included among the four that define the pipe, and hence these can be eliminated in the iteration. The relationship described above C1 + C2 * |TT| + C3 * VD + C4 * |Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv| – C8) * C9 Or a relationship that involves more communication C1 + C2 * |TT| + C3 * VD + C4 * | Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv| – C8) * C9 + (VD – C6) * (| Deqv| – C8) * C10 + (| Deqv| – C8) * (| Deqv| – C8) * C11 Refers to groove density VD. Groove density VD is the ratio of grooves NT in the pipe to the reference number Nref of the maximum number of grooves with a groove depth TT = 1.3 mm that can be inserted into the internal surface area of ​​a pipe with an equivalent diameter Deqv, expressed as a percentage. The invention can be applied to pipes with a wide range of inner surface diameters Di in which grooves are inserted. It is obvious that more grooves with a constant radius r2 of the circular arc at the base of the groove and a constant groove depth TT may be inserted in a pipe with a larger diameter Di than in a pipe with a smaller diameter Di. However, in order to be able to establish a relationship for all diameters, a normalization must be developed, in which what enters the relationship is no longer the actual number NT of grooves but the groove density VD. The groove density VD – as it is expressed in percentage – is obtained from the following equation: VD = NT / Nref*100 where the reference number Nref is the largest natural number for which the relationship It is established that Aeqv is the equivalent diameter calculated from formula (1) and that And in the case of that simultaneously it is possible to find an rNref which, by repeating that, is determined by reference to the equivalent diameter Aeqv calculated by formula (1), satisfies the following relations (also referred to as formula (2)): With secondary conditions , Nref can be easily determined by the following sequence of steps: In a first step, the right-hand side of the relation It is solved using the values ​​of the pipe to be examined to achieve the advantages of the invention. Since Nref must be a natural number, the natural number corresponding to the calculated value is assumed when the calculated value is a natural number, or the smaller natural number is closest to the calculated value. A pipe is taken as an example here with mm 60 = Di, mm 05 / 2 = TT, mm 8 = r2 and 8 = NT. This gives 4967769 / 19 ≥ Nref. Therefore Nref is assumed to be 19 in the first step. A second step checks whether with the Nref obtained in the first step it is possible to calculate an rNref with which, by referring to the equivalent diameter Aeqv calculated with formula (1), formula (2) can be satisfied without violating the following secondary condition: , Aeqv is solved with the values ​​of the pipe to be investigated for achieving the advantages of the invention, calculated using formula (1). Given the values ​​of the example above (mm 60 = Di, mm 05 / 2 = TT, mm 8 = r2 and 8 = NT), an Aeqvmm277397 / 2963 is obtained for the values ​​of the example given. Therefore, the second stage of the investigation for Nref is to investigate whether, with the Nref obtained in the first stage, it is possible to find an rNref such that, with Aeqv thus calculated, formula (2) is established and, at the same time, the secondary conditions mentioned are met. This iteration can be easily done with a spreadsheet program, for example Microsoft Excel and the "Goal Seek" function provided in the spreadsheet programs. A first empty cell is initially taken, which is then considered as the "variable cell" in the Goal Seek function. This cell is filled with any numerical value, for example |r1|. The above equation for Aeqv, which expresses Aeqv in terms of rNref, is then entered into a second cell, by referring to the first cell filled with any numerical value in terms of rNref, for example |r1|, and taking the value of r2 from the pipe characteristic data being examined to achieve the advantages of the invention. In a third cell, the equation "=Aeqv- value from second cell" is input, calculating Aeqv here with formula (1). The following equation is the input in a fourth cell: Where rNref refers to the first cell filled with any numerical value, for example |r1|, and the value of r2 is taken from the characteristic data of the pipe being examined to achieve the benefits of the invention. An if-then test is then added in a fifth cell, which gives the output word "FALSE" if the value in the fourth cell is less than zero and gives the output word "TRUE" otherwise. With the spreadsheet presented in this way, it is then possible to start the Goal Seek function foreseen in the spreadsheet program. The Goal Seek function asks which is the target cell. The third cell is given as input. The Goal Seek function also asks for the target value. This input is 0 (zero). The Goal Seek function also asks for the variable cell. The first cell is given as input. The Goal Seek function results in a value in the first cell. If the fifth cell contains "TRUE" for this value, the Nref found in the first step is decremented by 1 and a new Nref is thus formed, with which the second step is repeated. In general, even at the end of the Goal Seek function, this one value in the first cell results in the word "TRUE" also being present in the fifth cell, and so the new Nref thus obtained is the Nref that is to be used. Otherwise, the new Nref is again decremented by 1 and the second step is performed again.It has been found that, even when such a Goal Seek function in a spreadsheet program is not perfect in terms of decimal places, it does not have a significant impact on interpretation in any case due to the residual limit. With Nref thus found, for a pipe being considered for achieving the benefits of the invention, it is possible to determine the groove density VD from VD = NT / Nref100 *. If it is confirmed by the values ​​thus obtained that P1 * |Deqv|2+ P2 * |Deqv| + P3 = C1 + C2 * |TT| + C3 * VD + C4 * |Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv| – C8) * C9 Or, considering more connections, that P1 * | Deqv|2+ P2 * |Deqv| + P3 = C1 + C2 * |TT| + C3 * VD + C4 * | Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv| – C8) * C9 + (VD – C6) * (| Deqv| – C8) * C10 + (| Deqv| – C8) * (| Deqv| – C8) * C11, It is confirmed that the tube with these four tube characteristics (NT, Di, r2, TT), on which the calculation is based, improves the economic efficiency of thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. With the values ​​of the above example (mm 60 = Di, mm 05.2 = TT, mm 8 = r2 and 8 = NT), an Nref19 is obtained in the first step. In the second step, the Goal Seek function with Nref19 gives an rNref4509992 / 29. In the fourth cell, however, the value -0.07096658 results, and therefore the word "FALSE" is output in the fifth cell. If Nref19 is reduced by 1 to 18 and the second step is performed again, the Goal Seek function with Nref18 gives an rNref5192908 / 29. In the fourth cell, however, the value 10620948 results, and therefore the word "TRUE" is output in the fifth cell. 18 = Nref is the value used in the subsequent inspection of the pipe for compliance with the invention to calculate the groove density VD. The inventive tube extends along a longitudinal axis and has grooves inserted into its inner surface. The number of grooves present is expressed by the variable NT. The grooves extend in a spiral around the longitudinal axis along the inner surface of the tube. In a preferred embodiment, the grooves are distributed homogeneously over the circumference of the tube. This means that, in any cross-section at right angles to the longitudinal axis, for all grooves, the distance in the circumferential direction between two grooves in an adjacent arrangement is the same for all grooves. The groove depth is defined as the distance of the lowest point in the groove from the inner surface. This means, in a cross-section at right angles to the longitudinal axis, the shortest distance between the furthest removed point (the lowest point) in the groove, viewed from the longitudinal axis in the radial direction, and a circle of the inner surface about the longitudinal axis on which the inner surface portions furthest inwardly are arranged that remain between the grooves. Embodiments of the invention are contemplated in which the inner surface of the tube is cylindrical and the grooves are inserted into this cylindrical inner surface. In that case, the portions of the inner surface that form parts of a cylinder remain between the grooves. The circle of the inner surface on which the inner surface sections are arranged in the furthest inward position—since all remaining sections of the inner surface in this embodiment are arranged inwardly at the same distance—is the circle in cross-section on which the remaining sections of the cylindrical inner surface lie.But also embodiments are contemplated in which the remaining inner surface between the two grooves is reduced to almost a line because the groove opening (the opening of the groove cross-section in the inner surface area) is chosen to be very large. In particular, when, in such an embodiment, the curvature of the groove surface changes from a concave curvature at the groove base (a circular arc at the groove base) to a convex curvature of the groove surface in the region of the groove opening, the effect of such embodiments may be such that, in the circumferential direction, the grooves (in that case meaning the groove-convex curved region) are merged into an outer surface of the blade following the ribs arranged between the grooves (in that case meaning the groove-concave curved region) and the groove-limiting wall (or better: the groove-concave curved base) in the outer surface of the blade. The circle of the inner surface on which the inner surface portions furthest from the inner side are arranged, of course, is, in such embodiments, the circle in the cross-section on which the vertices of the "blades" in this cross-section lie. The depth of the groove is expressed by the variable TT in the relation which characterizes the tube found in accordance with the invention. In a preferred embodiment, the grooves have a circular cross-section in a cross-section at right angles to the longitudinal axis, at least at the base of the groove, which can preferably be approximated by a circular arc or correspond to a circular arc. In the region of the groove opening, the cross-sectional geometry of the groove can, in a preferred embodiment, be widened, in particular as a result of a change from a concave cross-sectional geometry at the base of the groove to a convex cross-sectional geometry in the region of the groove opening. In an alternative embodiment, in a cross-section at right angles to the longitudinal axis, the cross-sectional geometry of the entire groove can be approximated by a circular arc or correspond to a circular arc. Embodiments are likewise possible in which the groove has a cross-sectional geometry in a cross-section at right angles to the longitudinal axis that is a portion of an ellipse. In a preferred embodiment, the cross-sectional shape of a groove at right angles to the longitudinal axis remains the same for all cross-sectional areas at right angles to the longitudinal axis.In a particularly preferred embodiment, the shape and size of the cross-sectional area of ​​a groove at right angles to the longitudinal axis remain the same for all cross-sectional areas at right angles to the longitudinal axis. In a preferred embodiment, all grooves in the pipe have the same shape, and particularly preferably the same shape and size, in a cross-sectional area at right angles to the longitudinal axis, preferably in all cross-sectional areas at right angles to the longitudinal axis. If the grooves have different sizes and in particular different groove depths, the groove depth TT of the deepest groove is used for the relationship of the invention that characterizes the pipe. In a preferred embodiment, a cross-section of the pipe is rotationally symmetric about the longitudinal axis at right angles to the longitudinal axis. This means that there is at least one angle between ̊0 and ̊360 through which the cross-section of the pipe can be drawn by rotating about the longitudinal axis on itself. In a preferred embodiment, a cross-section of the tube at right angles to the longitudinal axis has point symmetry about the point occupied by the longitudinal axis in that cross-section. In a preferred embodiment, a cross-section of the tube at right angles to the longitudinal axis has mirror symmetry about an axis extending at right angles to the longitudinal axis and located in that cross-section. In a cross-section at right angles to the longitudinal axis, the tube has an inside diameter, denoted by the variable Di. The inside diameter is the diameter of the inner surface circle, i.e. the circle about the longitudinal axis, on which the inner surface sections furthest inward are arranged, remaining between the positions of the grooves. In a preferred embodiment, the cross-sectional area of ​​the tube inside has a diameter Di in a range of 15 mm to 280 mm, particularly preferably from 15 mm to 180 mm, particularly preferably from 20 mm to 150 mm and particularly preferably from 30 mm to 140 mm. In a preferred embodiment, the depth of the groove TT is in a range of 0.1 mm to 10 mm, particularly preferably from 0.1 mm to 7 mm and most preferably from 0.1 mm to 4 mm. In a preferred embodiment, the number of grooves NT is in a range from 1 to 100, particularly preferably from 2 to 50 and most preferably from 2 to 30. In a preferred embodiment, the VD groove density is in a range from 1% to 347%, particularly preferably from 2% to 113%, and most preferably from 10% to 105%. In a preferred embodiment, the grooves extend at an angle of from 20° to 40°, preferably from 22.5° to 32.5°, based on the longitudinal axis. In a preferred embodiment, in a cross-section at right angles to the longitudinal axis, the circular arc segment in the circle of the inner surface occupied by a portion of the inner surface arranged between two grooves is greater than 1% of the circular arc segment in the circle of the inner surface occupied by the groove opening of at least one of the adjacent grooves of this portion of the inner surface area, in particular greater than 2%, in particular greater than 5%, in particular greater than 10%, in particular greater than 30%, in particular greater than 50%, in particular greater than 70%. In a preferred embodiment, the circular arc segment in the circle of the inner surface occupied by the portion of the inner surface arranged between two grooves is equal to or greater than the circular arc segment in the circle of the inner surface occupied by the groove opening of at least one of the adjacent grooves of this portion of the inner surface. An inventive apparatus for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is directed through externally heated tubes, has at least one inventive tube. In the inventive tube, the heat source in the tube wall and in the inner part of the tube which inevitably varies along the tube circumference is in equilibrium between the bright side and the dark side, and the heat is transported rapidly inwards to the outer part of the core region. This is accompanied by a reduction in the risk of local overheating of the process gas in the tube wall and the resulting coke formation. Furthermore, the thermal stress on the tube material is lower due to the temperature compensation between the bright side and the dark side, which leads to an increase in the service life. Finally, in the case of the inventive tube, there is also a temperature homogenization along the tube cross-section with a result of a better olefin performance. The reason for this is that, without the inventive radial temperature compensation in the inner part of the tube, there would be a possibility of additional breakage in the hot tube wall and a very low reaction conversion in the middle of the tube. The inventive tube, depending on the material, can be produced, for example, from a centrifugally cast tube by twisting the ends of a tube with axially parallel grooves in opposite directions, or by producing an internal profile by performing a centrifugally cast tube, for example by hot forging, hot drawing or cold forming through a profile die, for example a floating mandrel or a mandrel bar or an external profile corresponding to the external profile of the tube, Cutting machines for the internal profiling of pipes are known in various forms, for example from German patent specification 280 23 195. These machines are also suitable for the production of a patented pipe. The inner surface of the inventive tube should have minimal roughness; therefore, it may be smoothed, for example mechanically polished or electrically smoothed. Pipe materials suitable for use in ethylene plants include nickel-chromium-iron alloys with 0.1% to 0.5% carbon, 20% to 35% chromium, 20% to 70% nickel, up to 3% silicon, up to 1% niobium, up to 5% tungsten, and additions of hafnium, titanium, rare earths, or zirconium, up to 0.5% in each case, and up to 6% aluminum. For the pipe, it is particularly preferable to use a nickel-chromium-iron alloy with high oxidation resistance and carburization resistance, tear resistance and creep resistance, which is composed of 0.05% to 0.6% carbon 20% to 50% chromium 5% to 40% iron Up to 6% aluminum Up to 2% silicon Up to 2% magnesium Up to 1.5% niobium Up to 1.5% tantalum Up to 0.6% tungsten Up to 0.1% titanium Up to 0.1% zirconium Up to 0.5% yttrium Up to 0.5% cerium Up to 0.5% molybdenum Up to 0.1% nitrogen Balance: Nickel containing impurities related to smelting. The following table shows possible embodiments of the invention, which are in accordance with the proposed relationship of the invention. In one row, for a selected inner diameter Deqv, a pair of NTMax, TTmin and VDmax is specified for a good heat transfer, but a lower heat transfer in relation to a second pair of NTMin, TTMax and VDmin. In addition, the table shows a heat transfer estimated by a simulation program ([W] Hmin(Deqv, TTmin, VDMax)) for a lower heat transfer; ([W] HMax(Deqv, TTmax, VDmin)) for a more-improved heat transfer. [W] Hmin(Deqv, TTmin, VDmax) TTmin VDmax NTmax Deqv No. 95559 / 10831 3 / 1 100 9 35 1 96106 / 12288 3 / 1 100 11 40 2 69121 / 13732 3 / 1 100 12 45 3 14603 / 15163 3 / 1 100 14 50 4 32553 / 16580 3 / 1 100 16 55 5 2297 / 17984 3 / 1 100 18 60 6 85855 / 19374 3 / 1 100 20 65 7 21208 / 20752 3 / 1 100 21 70 8 29028 / 22116 3 / 1 100 23 75 9 09315 / 23467 3 / 1 100 25 80 10 62071 / 24804 3 / 1 100 27 85 11 87294 / 26128 3 / 1 100 29 90 12 84984 / 27439 3 / 1 100 30 95 13 55142 / 28737 3 / 1 100 32 100 14 97768 / 30021 3 / 1 100 34 105 15 12861 / 31293 3 / 1 100 36 110 16 00422 / 32551 3 / 1 100 38 115 17 6045 / 33795 3 / 1 100 39 120 18 92946 / 35026 3 / 1 100 41 125 19 9791 / 36244 3 / 1 100 43 130 20 75341 / 37449 3 / 1 100 45 135 21 25239 / 38641 3 / 1 100 47 140 22 4951 / 43274 3 / 1 100 54 160 23 33262 / 47695 3 / 1 100 61 180 24 76496 / 51903 3 / 1 100 68 200 25 44243 / 66613 3 / 1 100 97 280 26 [W] Hmin(Deqv, TTmin, VDmax) TTmin VDmax NTmax Deqv No. 65262 / 11564 7 / 2 33333333 / 33 3 35 27 35209 / 13032 7 / 2 27272727 / 27 3 40 28 96054 / 14463 7 / 2 25 3 45 29 80079 / 15887 7 / 2 42857143 / 21 3 50 30 40888 / 17292 7 / 2 75 / 18 3 55 31 77042 / 18679 7 / 2 66666667 / 16 3 60 32 07678 / 20051 7 / 2 15 3 65 33 40771 / 21404 7 / 2 28571429 / 14 3 70 34 18795 / 22746 7 / 2 04347826 / 13 3 75 35 38983 / 24073 7 / 2 12 3 80 36 30292 / 25386 7 / 2 11111111 / 11 3 85 37 1369 / 26685 7 / 2 34482759 / 10 3 90 38 09023 / 27969 7 / 2 10 3 95 39 37497 / 29240 7 / 2 375 / 9 3 100 40 91084 / 30497 7 / 2 823529412 / 8 3 105 41 77677 / 31741 7 / 2 333333333 / 3 3 110 42 03508 / 32972 7 / 2 894736842 / 7 3 115 43 38764 / 34188 7 / 2 692307692 / 7 3 120 44 6438 / 35391 7 / 2 317073171 / 7 3 125 45 40387 / 36581 7 / 2 976744186 / 6 3 130 46 6973 / 37757 7 / 2 666666667 / 6 3 135 47 54851 / 38920 7 / 2 382978723 / 6 3 140 48 89962 / 43437 7 / 2 555555556 / 5 3 160 49 49693 / 47741 7 / 2 918032787 / 4 3 180 50 75693 / 51831 7 / 2 411764706 / 4 3 200 51 32146 / 66063 7 / 2 092783505 / 3 3 280 52 It is found that the expected heat transfer, both for a good but slightly lower value in relation to the more-optimized value ([W] Hmin(Deqv, TTmin, VDMax)) and for a more-optimized value ([W] HMax(Deqv, TTmax, VDmin)), can be plotted in direct proportion to the inner diameter, as shown in Figure 4. The table below shows the values ​​of the various variables of the relationships used according to the invention for individual tubes. The circular arc at the base of the groove has a radius r2mm 8. Row Aeqv A1 AT r1 b1 b2 sh 1 113 / 962 691 / 870 158 / 10 648 / 16 365 / 11 331 / 12 146 / 11 961 / 0 2 637 / 1256 789 / 1149 713 / 9 131 / 19 883 / 10 77 / 11 737 / 10 769 / 0 3 431 / 1590 643 / 1477 399 / 9 688 / 21 543 / 10 374 / 11 44 / 10 638 / 0 4 495 / 1963 026 / 1835 176 / 9 168 / 24 303 / 10 093 / 11 226 / 10 547 / 0 5 829 / 2375 74 / 2231 006 / 9 653 / 26 12 / 10 878 / 10 059 / 10 479 / 0 6 433 / 2827 765 / 2667 87 / 8 141 / 29 975 / 9 708 / 10 927 / 9 426 / 0 7 307 / 3318 09 / 3143 761 / 8 63 / 31 858 / 9 57 / 10 818 / 9 383 / 0 8 451 / 3848 405 / 3666 669 / 8 162 / 34 76 / 9 455 / 10 727 / 9 348 / 0 9 865 / 4417 229 / 4220 593 / 8 652 / 36 679 / 9 359 / 10 65 / 9 319 / 0 10 548 / 5026 348 / 4813 528 / 8 143 / 39 609 / 9 278 / 10 585 / 9 295 / 0 11 502 / 5674 756 / 5445 472 / 8 635 / 41 55 / 9 207 / 10 529 / 9 274 / 0 12 725 / 6361 451 / 6117 423 / 8 128 / 44 498 / 9 146 / 10 48 / 9 255 / 0 13 218 / 7088 823 / 6836 38 / 8 65 / 46 452 / 9 092 / 10 436 / 9 239 / 0 14 982 / 7853 043 / 7587 342 / 8 143 / 49 411 / 9 044 / 10 397 / 9 225 / 0 15 015 / 8659 545 / 8376 308 / 8 637 / 51 375 / 9 001 / 10 362 / 9 213 / 0 16 318 / 9503 329 / 9205 277 / 8 131 / 54 343 / 9 963 / 9 331 / 9 201 / 0 17 891 / 10386 393 / 10073 25 / 8 626 / 56 314 / 9928 / 9 303 / 9 191 / 0 18 734 / 11309 968 / 10988 225 / 8 143 / 59 287 / 9 897 / 9 278 / 9 182 / 0 19 846 / 12271 564 / 11935 202 / 8 638 / 61 263 / 9 868 / 9 254 / 9 174 / 0 20 229 / 13273 438 / 12921 181 / 8 133 / 64 241 / 9 842 / 9 233 / 9 166 / 0 21 882 / 14313 589 / 13946 162 / 8 628 / 66 221 / 9 818 / 9 213 / 9 159 / 0 22 804 / 15393 017 / 15011 144 / 8 124 / 69 202 / 9 796 / 9 195 / 9 153 / 0 23 193 / 20106 568 / 19669 086 / 8 127 / 79 14 / 9 722 / 9 135 / 9 132 / 0 24 9 / 25446 406 / 24956 041 / 8 128 / 89 092 / 9 666 / 9 088 / 9 116 / 0 25 927 / 31415 542 / 30871 006 / 8 13 / 99 055 / 9 621 / 9 052 / 9 103 / 0 26 216 / 61575 235 / 60807 917 / 7 124 / 139 962 / 8 511 / 9 96 / 8 072 / 0 27 113 / 962 692 / 877 14 / 28 715 / 16 619 / 14 379 / 17 158 / 14 573 / 1 28 637 / 1256 212 / 1175 142 / 27 341 / 19 145 / 14 706 / 16 832 / 13 279 / 1 29 431 / 1590 08 / 1511 45 / 26 932 / 21 82 / 13 241 / 16 592 / 13 08 / 1 30 495 / 1963 673 / 1885 941 / 25 5 / 24 582 / 13 899 / 15 409 / 13 935 / 0 31 829 / 2375 186 / 2299 548 / 25 053 / 27 4 / 13 636 / 15 263 / 13 825 / 0 32 433 / 2827 727 / 2751 236 / 25 596 / 29 255 / 13 426 / 15 145 / 13 739 / 0 33 307 / 3318 365 / 3243 981 / 24 131 / 32 138 / 13 256 / 15 047 / 13 669 / 0 34 451 / 3848 144 / 3774769 / 24 66 / 34 041 / 13 114 / 15 964 / 12 612 / 0 35 865 / 4417 095 / 4344 59 / 24 186 / 37 959 / 12 994 / 14 894 / 12 563 / 0 36 548 / 5026 239 / 4953 437 / 24 707 / 39 889 / 12 891 / 14 833 / 12 522 / 0 37 502 / 5674 591 / 5601 304 / 24 226 / 42 829 / 12 802 / 14 779 / 12 486 / 0 38 725 / 6361 163 / 6289 187 / 24 743 / 44 776 / 12 724 / 14 732 / 12 455 / 0 39 218 / 7088 965 / 7015 085 / 24 257 / 47 729 / 12 656 / 14 691 / 12 428 / 0 40 982 / 7853 002 / 7782 993 / 23 77 / 49 688 / 12 595 / 14 653 / 12 404 / 0 41 015 / 8659 28 / 8587 912 / 23 282 / 52 651 / 12 54 / 14 62 / 12 382 / 0 42 318 / 9503 804 / 9431 838 / 23 739 / 54 617 / 12 491 / 14 589 / 12 363 / 0 43 891 / 10386 577 / 10315 771 / 23 302 / 57 587 / 12 446 / 14 562 / 12 345 / 0 44 734 / 11309 601 / 11238 711 / 23 811 / 59 56 / 12 406 / 14 537 / 12 329 / 0 45 846 / 12271 88 / 12200 565 / 23 319 / 62 535 / 12 369 / 14 514 / 12 315 / 0 46 229 / 13273 415 / 13202 605 / 23 826 / 64 512 / 12 335 / 14 493 / 12 302 / 0 47 882 / 14313 208 / 14243 558 / 23 333 / 67 491 / 12 304 / 14 473 / 12 289 / 0 48 804 / 15393 26 / 15323 515 / 23 839 / 69 472 / 12 275 / 14 455 / 12 278 / 0 49 193 / 20106 081 / 20036 371 / 23 86 / 79 407 / 12 178 / 14 394 / 12 241 / 0 50 9 / 25446 119 / 2537726 / 23 877 / 89 357 / 12 105 / 14 347 / 12 212 / 0 51 927 / 31415 407 / 31346 173 / 23 889 / 99 318 / 12 046 / 14 31 / 12 19 / 0 52 216 / 61575 358 / 61506 953 / 22 922 / 139 22 / 12 899 / 13 216 / 12 133 / 0 In the CFD (Computational Fluid Dynamics) analysis used to estimate the values ​​of ([W] Hmin(Deqv, TTmin, VDMax)) and ([W] HMax(Deqv, TTmax, VDmin)), the following simulation conditions were used: Boundary conditions for heat transfer simulation: Space temperature for external heating of pipes: 1300 °C Emissivity ε of tubes: 0.85 Including light / dark sides (light side: 80% radiation 20% convection; dark side: 20% radiation 80% convection) and the physical properties of the materials density, specific heat capacity, and thermal conductivity as a function of temperature Simulation length: m 2 Table 1: Feed mixture state at the pipe inlet Parameter value 621 Temperature, ˚C 2 Pressure, bar 8 / 52912 Specific-surface mass flow rate, g / (s.m2) Table 2: Physical properties of feed mixture Thermal conductivity W / mK Dynamic viscosity kg / ms Specific heat capacity kJ / kgK Density kg / m³ Temperature ˚C 08947538 / 0 941481 / 2 E 05- 81553015 / 2 87467615 / 0 620 09122076 / 0 974235 / 2 E 05- 82698110 / 2 86669998 / 0 630 09296613 / 0 006989 / 3 E 05- 83843205 / 2 85872380 / 0 640 09471151 / 0 039743 / 3 E 05- 84988300 / 2 85074763 / 0 650 09645688 / 0 072497 / 3 E 05- 86133395 / 2 84277145 / 0 660 09820226 / 0 105251 / 3 E 05- 87278490 / 2 83479528 / 0 670 09994763 / 0 138005 / 3 E 05- 88423585 / 2 82681910 / 0 680 10169301 / 0 170759 / 3 E 05- 89568680 / 2 81884293 / 0 690 10343838 / 0 203513 / 3 E 05- 90713775 / 2 81086675 / 0 700 10518376 / 0 236268 / 3 E 05- 91858870 / 2 80289058 / 0 710 10692913 / 0 269022 / 3 E 05- 93003965 / 2 79491440 / 0 720 10867451 / 0 301776 / 3 E 05- 94149060 / 2 78693823 / 0 730 11041988 / 0 334530 / 3 E 05- 95294155 / 2 77896205 / 0 740 11216526 / 0 367284 / 3 E 05- 96439250 / 2 77098588 / 0 750 11391063 / 0 400038 / 3 E 05- 97584345 / 2 76300970 / 0 760 11565601 / 0 432792 / 3 E 05- 98729440 / 2 75503353 / 0 770 11740138 / 0 465546 / 3 E 05- 99874535 / 2 74705735 / 0 780 11914676 / 0 498300 / 3 E05- 01019630 / 3 73908118 / 0 790 12089213 / 0 531055 / 3 E 05- 02164725 / 3 73110500 / 0 800 12263751 / 0 563809 / 3 E 05- 03309820 / 3 72312883 / 0 810 12438288 / 0 596563 / 3 E 05- 04454915 / 3 71515265 / 0 820 12612826 / 0 629317 / 3 E 05- 05600010 / 3 70717648 / 0 830 0.12787363 662071 / 3 E 05- 06745105 / 3 69920030 / 0 840 12961901 / 0 694825 / 3 E 05- 07890200 / 3 69122413 / 0 850 The inventive tube is preferably used for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is passed through externally heated tubes. The invention is illustrated in detail by a drawing which merely shows embodiments of the invention. The drawing shows: Figure 1. A perspective view of an inventive tube, Figure 2. A possible first cross-section of an inventive tube in a cross-sectional plane at right angles to the longitudinal axis of the tube, Figure 3. A second possible cross-section of an inventive tube in a cross-sectional plane at right angles to the longitudinal axis of the tube, Figure 4. A diagram showing, for a pair of numbers of grooves NT and groove depths TT that lead to good results and a pair of numbers of grooves NT and groove depths TT that lead to more-improved results, the dependence of the heat transfer resulting from this pair on the inner diameter and Figure 5. A cross-section along the length of an inventive tube with a groove. The tube 1 of the invention shown in Figure 1 extends along a longitudinal axis A and has a number 3 of grooves 2 inserted into the inner surface which extend in a spiral around the longitudinal axis A along the inner surface. In the cross-section of the tube 1 of the invention shown in Figure 2, it is evident that, in a preferred embodiment, grooves 2 are inserted in the cylindrical inner surface of the tube 1 in a different manner. Between the grooves 2, therefore, portions of the cylindrical inner surface of the tube 1 remain. Included in Figure 2 are the groove depth TT and the diameter Di and the inner surface circle 3. Figure 2 also shows that the cross-section of the grooves 2 can be represented by a circular arc. In the cross-section of the inventive tube 1 shown in Figure 3, it is evident that in an alternative embodiment, the concave grooves at the base of the groove 4 can merge into a convex shape in the direction of the opening of the groove 5, and the portion of the inner surface remaining between the two grooves 2 is reduced to approximately a line. Included in Figure 3 are the groove depth TT and the diameter Di and the inner surface circle 3. Figure 4 shows the values ​​of ([W] Hmin(Deqv, TTmin, VDMax)) and ([W] HMax(Deqv, TTmax, VDmin)) reported in the table as a function of the equivalent diameter of Deqv. Obviously, these values ​​can be represented by a line in each case. Figure 5 and the detail Y shown in Figure 5, for example, in an inventive tube with a groove, show the nomenclature abbreviations A1, r1, TT, h, b2, b1, AT, r2 and s used in the claims and this description. The method in which the four values ​​NT, Di, r2 and TT determine the pipe that may be found can be illustrated by the following examples. In one example, there is the external requirement that the passage area corresponds to a smooth tube with a diameter of 60 mm. Furthermore, from a production point of view, the tools available for tube production lead to the constraint that a groove depth TT of 1.3 mm and a radius r2 of the circular arc of the groove base of 8 mm must be chosen in the case of grooves with a cross-section in the shape of a circular arc. The question is what diameter Di and what number of grooves can improve the economic efficiency of thermal cracking of hydrocarbons in tube furnaces with externally heated tubes. The starting point is as follows: Deqv= 60 mm Aeqv=π(2 / 60)2=2827. 43 mm2 TT = 1.3 mm r2= 8 mm Aeqv directly gives mm 30 = 2 / Dieqv= reqv r2 and reqv, to determine Nref in the first step with the formula A first Nref gives 18. With this Nref18, the Goal Seek function described above gives an rNref1406241 / 29, although the second condition , is satisfied simultaneously. The number 18 should thus be used as Nref. 18 = Nref gives 100*18 / NT= VD. Enter the minimum values ​​of P1, P2, and P3 for the left-hand side of the equation. P1 * | Deqv|2+ P2 * | Deqv| + P3 = C1 + C2 * |TT| + C3 * VD + C4 * | Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv| – C8) * C9 + (VD – C6) * (| Deqv| – C8) * C10 + (| Deqv| – C8) * (| Deqv| – C8) * C11 With constants C1 = 066 / 1946 C2 = 378 / 302 C3 = -178 / 2 C4 = 002 / 266 C5 = 954 / 1 C6 = 495 / 50 C7 = -2 / 004 C8 = 732 / 79 C9 = -1 / 041 C10 = 0.04631 C11 = 26550 / 0- -0.2 ≥ P1 ≥ -0.3 310 ≤ P2 ≤ 315 200 ≤ P3 ≤ 1500 Gives the amount P1 * |Deqv|2+ P2 * |Deqv| + P3 = - 0.3 * (60)2 + 310 * 60 + 200 = 17720 And entering the maximum values ​​of P1, P2, and P3 for the left-hand side of the equation gives, P1 * |Deqv|2+ P2 * |Deqv| + P3 = - 0.2 * (60)2 + 315 * 60 + 1500 = 19680 For the expression on the right side of the equation C1 + C2 * |TT| + C3 * VD + C4 * |Deqv| + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv| – C8) * C9 + (VD – C6) * (|Deqv| – C8) * C10 + (|Deqv| – C8) * (|Deqv| – C8) * C11 Entering 3 / 1 = |TT| and 60 = |Deqv| gives 066 / 1946 + 378 / 302 * 3 / 1 + - 178 / 2 * VD + 002 / 266 * 60 + (1 / 3 – 954 / 1) * (VD – 50 / 495) * - 2 / 004 + ( 3 / 1 – 954 / 1 ) * ( 60 – 732 / 79 ) * - 041 / 1 + (VD-495 / 50) * (79-732-60) * 04631 / 0 + ( 60 – 732 / 79 ) * ( 60 – 732 / 79 ) * - 26550 / 0 And so: 4329 / 18162 – 7812 / 1 VD And with NT5556 / 5 = 100 * 18 / NT= 100 * Nref / NT= VD the result is this 4329 / 18162 – 8954 / 9 NT In order to ensure that the tube achieves the benefits of the invention, NT must be chosen such that the relationship 19680 ≥ 4329 / 18162 – 8954 / 9 NT And the relationship 4329 / 18162 – 8954 / 9 NT≥ 17720 are satisfied. Both relations are satisfied with 71 / 44 ≥ NT≥ 1. Since the NT thus obtained is larger than the parameter Nref calculated previously, even in the case of applying the maximum possible number of grooves (Nref = 18), the advantages of the invention can still be achieved at this valley depth. The user is therefore free in this example to deliver the pipe worker up to the maximum possible number of grooves without losing the advantages of the invention. The NT thus found can be used to iteratively determine the radius r1 of the pipe and hence the internal diameter (r12 =) Di of the pipe using formula (1), since Aeqv = 2827 / 243 mm. Therefore, it is possible to determine all the parameters required for producing a pipe that implements the advantages of the invention.

Claims

Claims:

1. A pipe for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is guided through externally heated pipes, wherein  the pipe (1) extends along a longitudinal axis (A) and has a number NT of grooves (2) that have been introduced into the inner surface of the pipe (1) and extend in a helix around the longitudinal axis (A) along the inner surface,  the inner surface into which the grooves (2) have been introduced, in a cross section at right angles to the longitudinal axis (A), has a diameter Di and a radius r1 = Di / 2,  the grooves (2) in the cross section at right angles to the longitudinal axis (A), in their groove base (4), each have the form of a circular arc and the circular arc has a radius r2 , the grooves (2) each have a groove depth TT which, in the cross section at right angles to the longitudinal axis (A), corresponds in each case to the smallest distance between the circle having the diameter Di on which the inner surface lies and the center of which lies on the longitudinal axis (A), and the furthest removed point of the groove base (4) of the groove (2) from the longitudinal axis (A), wherein the numerical value |Deqv | of an equivalent diameter Deqv and the number NT of grooves (2) and the numerical value |TT| of the groove depth TT of the grooves (2) measured in mm satisfy the relationship P1 * |Deqv |2 + P2 * |Deqv | + P3 = C1 + C2 * |TT| + C3 * VD + C4 * |Deqv | + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (|Deqv | – C8) * C9 with the constants C1 = 1946.066 C2 = 302.378 C3 = -2.178 C4 = 266.002 C5 = 1.954 C6 = 50.495 C7 = -2.004 C8 = 79.732 C9 = -1.041 -0.2 ≥ P1 ≥ -0.3 310 ≤ P2 ≤ 315 200 ≤ P3 ≤ 1500, where the groove density VD that describes the ratio of the grooves NT in the pipe in relation to the reference number Nref of the maximum number of grooves having a groove depth TT = 1.3 mm that can be introduced in the inner surface area of a pipe having the same equivalent diameter Deqv in percent is found from the following relationship: VD = NT / Nref * 100 and the reference number Nref is the greatest natural number that satisfies the relationship where and for which there is an rNref which, with reference to the value of Aeqv ascertained by the above relationship, satisfies the following conditions that Aeqv is likewise without infringing the boundary conditions , and where the equivalent diameter Deqv is found from the relationship Deqv = 2 reqv , wherein the inner surface of the pipe is cylindrical and the grooves are introduced into this cylindrical inner surface in such a way that portions of the inner surface that form a cylinder remain between the grooves.

2. A pipe for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is guided through externally heated pipes, wherein  the pipe (1) extends along a longitudinal axis (A) and has a number NT of grooves (2) that have been introduced into the inner surface of the pipe (1) and extend in a helix around the longitudinal axis (A) along the inner surface,  the inner surface into which the grooves (2) have been introduced, in a cross section at right angles to the longitudinal axis (A), has a diameter Di and a radius r1 = Di / 2,  the grooves (2) in the cross section at right angles to the longitudinal axis (A), in their groove base (4), each have the form of a circular arc and the circular arc has a radius r2 , the grooves (2) each have a groove depth TT which, in the cross section at right angles to the longitudinal axis (A), corresponds in each case to the smallest distance between the circle having the diameter Di on which the inner surface lies and the center of which lies on the longitudinal axis (A), and the furthest removed point of the groove base (4) of the groove (2) from the longitudinal axis (A), wherein the numerical value |Deqv | of an equivalent diameter Deqv and the number NT of grooves (2) and the numerical value |TT| of the groove depth TT of the grooves (2) measured in mm satisfy the relationship P1 * |Deqv |2 + P2 * |Deqv | + P3 = C1 + C2 * |TT| + C3 * VD + C4 * | Deqv | + (|TT| – C5) * (VD – C6) * C7 + (|TT| – C5) * (| Deqv | – C8) * C9 + (VD – C6) * (| Deqv | – C8) * C10 + (| Deqv | – C8) * (| Deqv | – C8) * C11 with the constants C1 = 1946.066 C2 = 302.378 C3 = -2.178 C4 = 266.002 C5 = 1.954 C6 = 50.495 C7 = -2.004 C8 = 79.732 C9 = -1.041 C10 = 0.04631 C11 = -0.26550 -0.2 ≥ P1 ≥ -0.3 310 ≤ P2 ≤ 315 200 ≤ P3 ≤ 1500, where the groove density VD that describes the ratio of the grooves NT in the pipe in relation to the reference number Nref of the maximum number of grooves having a groove depth TT = 1.3 mm that can be introduced in the inner surface area of a pipe having the same equivalent diameter Deqv in percent is found from the following relationship: VD = NT / Nref * 100 and the reference number Nref is the greatest natural number that satisfies the relationship where and for which there is an rNref which, with reference to the value of Aeqv ascertained by the above relationship, satisfies the following conditions that Aeqv is likewise without infringing the boundary conditions , and where the equivalent diameter Deqv is found from the relationship Deqv = 2 reqv , wherein the inner surface of the pipe is cylindrical and the grooves are introduced into this cylindrical inner surface in such a way that portions of the inner surface that form a cylinder remain between the grooves.

3. The pipe as claimed in any of claims 1 and 2, wherein , in a cross section at right angles to the longitudinal axis, the circular arc segment in the inner surface circle occupied by a portion of the inner surface arranged between two grooves is greater than 1% of the circular arc segment in the inner surface circle occupied by the groove opening of at least one of the grooves adjoining this portion of the inner surface area.

4. The pipe as claimed in any of claims 1 to 3, wherein the diameter Di of the inner surface into which the grooves (2) have been introduced is within a range from 15 mm to 280 mm.

5. The pipe as claimed in any of claims 1 to 4, wherein the groove depth TT is within a range from 0.1 mm to 10 mm.

6. The pipe as claimed in any of claims 1 to 5, wherein the number NT of grooves (2) results in a groove density within a range from 1% to 347%.

7. The pipe as claimed in any of claims 1 to 6, wherein the grooves (2) run at an angle of 20° to 40°, preferably of 22.5° to 32.5°, based on the longitudinal axis (A).

8. The pipe as claimed in any of claims 1 to 7, wherein the pipe is a centrifugally cast pipe or has been produced from a centrifugally cast pipe by introducing grooves into a centrifugally cast pipe.

9. The pipe as claimed in any of claims 1 to 8, wherein the pipe includes a nickel-chromium-iron alloy having high oxidation and carburization resistance, rupture resistance and creep resistance, composed of 0.05% to 0.6% carbon 20% to 50% chromium 5% to 40% iron 2% to 6% aluminum up to 2% silicon up to 2% manganese up to 1.5% niobium up to 1.5% tantalum up to 6.0% tungsten up to 1.0% titanium up to 1.0% zirconium up to 0.5% yttrium up to 0.5% cerium up to 0.5% molybdenum up to 0.1% nitrogen balance: nickel including melting-related impurities, and especially consists of such an alloy.

10. An apparatus for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is guided through externally heated pipes, characterized by a pipe as claimed in any of claims 1 to 9.

11. The use of a pipe as claimed in any of claims 1 to 10 for thermal cracking of hydrocarbons in the presence of steam, in which the feed mixture is guided through externally heated pipes.

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